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Title: Layered nested Markov chain Monte Carlo

Abstract

A configurational sampling algorithm based on nested layerings of Markov chains (Layered Nested Markov Chain Monte Carlo or L-NMCMC) is presented for simulations of systems characterized by rugged free energy landscapes. The layerings are generated using a set of auxiliary potential energy surfaces. The implementation of the method is demonstrated in the context of a rugged, two-dimensional potential energy surface. The versatility of the algorithm is next demonstrated on a simple, many body system, namely, a canonical Lennard-Jones fluid in the liquid state. In that example, different layering schemes and auxiliary potentials are used, including variable cutoff distances and excluded volume tempering. In addition to calculating a variety of properties of the system, it is also shown that L-NMCMC, when combined with a free-energy perturbation formalism, provides a straightforward means to construct approximate free-energy surfaces at no additional computational cost using the sampling distributions of each auxiliary Markov chain. In conclusion, the proposed L-NMCMC scheme is general in that it could be complementary to any number of methods that rely on sampling from a target distribution or methods that exploit a hierarchy of time scales and/or length scales through decomposition of the potential energy.

Authors:
 [1];  [1];  [1]
  1. Argonne National Lab. (ANL), Lemont, IL (United States); Univ. of Chicago, Chicago, IL (United States)
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE
OSTI Identifier:
1466393
Alternate Identifier(s):
OSTI ID: 1457211
Grant/Contract Number:  
AC02-06CH11357
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 149; Journal Issue: 7; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Jackson, Nicholas E., Webb, Michael A., and de Pablo, Juan J. Layered nested Markov chain Monte Carlo. United States: N. p., 2018. Web. doi:10.1063/1.5030531.
Jackson, Nicholas E., Webb, Michael A., & de Pablo, Juan J. Layered nested Markov chain Monte Carlo. United States. doi:10.1063/1.5030531.
Jackson, Nicholas E., Webb, Michael A., and de Pablo, Juan J. Tue . "Layered nested Markov chain Monte Carlo". United States. doi:10.1063/1.5030531.
@article{osti_1466393,
title = {Layered nested Markov chain Monte Carlo},
author = {Jackson, Nicholas E. and Webb, Michael A. and de Pablo, Juan J.},
abstractNote = {A configurational sampling algorithm based on nested layerings of Markov chains (Layered Nested Markov Chain Monte Carlo or L-NMCMC) is presented for simulations of systems characterized by rugged free energy landscapes. The layerings are generated using a set of auxiliary potential energy surfaces. The implementation of the method is demonstrated in the context of a rugged, two-dimensional potential energy surface. The versatility of the algorithm is next demonstrated on a simple, many body system, namely, a canonical Lennard-Jones fluid in the liquid state. In that example, different layering schemes and auxiliary potentials are used, including variable cutoff distances and excluded volume tempering. In addition to calculating a variety of properties of the system, it is also shown that L-NMCMC, when combined with a free-energy perturbation formalism, provides a straightforward means to construct approximate free-energy surfaces at no additional computational cost using the sampling distributions of each auxiliary Markov chain. In conclusion, the proposed L-NMCMC scheme is general in that it could be complementary to any number of methods that rely on sampling from a target distribution or methods that exploit a hierarchy of time scales and/or length scales through decomposition of the potential energy.},
doi = {10.1063/1.5030531},
journal = {Journal of Chemical Physics},
number = 7,
volume = 149,
place = {United States},
year = {Tue Jun 26 00:00:00 EDT 2018},
month = {Tue Jun 26 00:00:00 EDT 2018}
}

Journal Article:
Free Publicly Available Full Text
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